o
    8VaJ]                    @   s  d Z ddlmZ edZer ddlmZmZmZmZ ddlm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z mZmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmHZHmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmÐZÐmĐZĐmŐZŐmƐZƐmǐZǐmZmȐZȐmɐZɐmʐZʐmːZːm̐Z̐m͐Z͐mΐZΐmϐZϐmАZАmѐZѐmҐZҐmӐZӐmԐZԐmՐZՐm֐Z֐mאZאmؐZؐmِZِmڐZڐmېZېmܐZݐmސZߐmZmZmZ ddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ ddlmZ ddlmZmZ dd	lmZmZmZmZmZmZmZm Z  dd
lmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZ ddlmZmZmZmZmZmZmZ ddlmZ dd dD \ZZZZZZZZZ Z!Z"Z#Z$Z%Z&Z'Z(Z)Z*Z+Z,Z-Z.Z/Z0Z1Z2Z3Z4Z5Z6dd dD \Z7Z8Z9Z:Z;Z<Z=Z>Z?Z@ZAZBZCZDZEZFZ?Z@ZGZHZIZJZKZLZMZNZOZPZQZRed\	ZSZTZUZVZWZXZYZZZ[dZ\dZ]dZ^dd Z_dd Z`dd Zadd Zbdd Zcdd  Zdd!d" Zed#d$ Zfd%d& Zgd'd( Zhd)d* Zid+d, Zjd-d. Zkd/d0 Zld1d2 Zmd3d4 Znd5d6 Zod7d8 Zpd9d: Zqd;d< Zrd=d> Zsd?d@ ZtdAdB ZudCdD ZvdEdF ZwdGdH ZxdIdJ ZydKdL ZzdMdN Z{dOdP Z|dQdR Z}dSdT Z~dUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddĄ ZddƄ ZddȄ Zddʄ Zdd̄ Zdd΄ ZddЄ Zdd҄ ZddԄ Zddք Zdd؄ Zddڄ Zdd܄ Zddބ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  ZԐdd ZՐdd Z֐dd Zאdd Zؐd	d
 Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX Z dYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Z	dkdl Z
dmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Z dd Z!dS (  z
This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)IntegralSsqrtAndOrIntegerFloatModIAbssimplifyMulAddPowsign
EulerGammaWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  N/usr/lib/python3/dist-packages/sympy/integrals/rubi/rules/special_functions.py
<listcomp>       r  ZABCFGHabcdefghijklmnpqrtuvswxyzc                 C   r  r  r  r  r  r  r  r     r  )Za1Za2Zb1Zb2Zc1Zc2Zd1Zd2n1n2Ze1Ze2f1f2Zg1Zg2r  r  Zn3ZPqZPmZPxZQmZQrZQxZjnZmnZnon2ZRFxZRGxzi ii Pqq Q R r C k uFNc                 C   svP  ddl m} m}m}m}m}m}m}m}m	}m
}	m}
m}m}m}m}m}m}m}m}m}m}m}m}m}m}m}m}m}m}m}m}m }m!} m"}!m#}"m$}#m%}$m&}%m'}&m(}'m)}(m*})m+}*m,}+m-},m.}-m/}.m0}/m1}0m2}1m3}2m4}3m5}4m6}5m7}6m8}7m9}8m:}9m;}:m<};m=}<m>}=m?}>m@}?mA}@mB}AmC}BmD}CmE}DmF}EmG}FmH}GmI}HmJ}ImK}JmL}KmM}LmN}MmO}NmP}OmQ}PmR}QmS}RmT}SmU}TmV}UmW}VmX}WmY}XmZ}Ym[}Zm\}[m]}\ t^t_t`tatbdtcd tbdtcd ta||| }]td|]te}^t^t_tftatbdtcd tbdtcd ta||| }_td|_tg}`t^t_thtatbdtcd tbdtcd ta||| }atd|ati}bt^t_t`tatbdtcd ta ta||}ctd|ctj}dt^t_tftatbdtcd ta ta||}etd|etk}ft^t_thtatbdtcd ta ta||}gtd|gtl}ht^t_tatbdtcd t`tatbdtcd tbdtcd  ta||||}itd|itm}jt^t_tatbdtcd tftatbdtcd tbdtcd  ta||||}ktd|ktn}lt^t_tatbdtcd thtatbdtcd tbdtcd  ta||||}mtd|mto}nt^t_tat`tatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta|||||}otd|otq}pt^t_tatftatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta|||||}qtd|qtr}rt^t_tathtatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta|||||}std|sts}tt^t_tatt t`tatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta||||||	}utd|utu}vt^t_tatt tftatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta||||||	}wtd|wtv}xt^t_tatt thtatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta||||||	}ytd|ytw}zt^t_t`tatbdtcd tptatcd tbdtcd tbd	tcd  ta ta||
}{td|{tx}|t^t_tftatbdtcd tptatcd tbdtcd tbd	tcd  ta ta||
}}td|}ty}~t^t_thtatbdtcd tptatcd tbdtcd tbd	tcd  ta ta||}td|tz}t^t_tatt t`tatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta||||||}td|t{}t^t_tatt tftatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta||||||}td|t|}t^t_tatt thtatbdtcd tbdtcd  tptatcd tbdtcd tbd	tcd  ta||||||}td|t}}t^t_t`tatbdtcd tbdtcd tcd ta||| }td|t~}t^t_tftatbdtcd tbdtcd tcd ta||| }td|t}t^t_thtatbdtcd tbdtcd tcd ta||| }td|t}t^t_tatbdtcd t`tatbdtcd tcd  ta||||}td|t}t^t_tatbdtcd tftatbdtcd tcd  ta||||}td|t}t^t_tatbdtcd thtatbdtcd tcd  ta||||}td|t}t^t_tatbdtcd t`ttatbdtcd  tcd  ta|||}td|t}t^t_tatbdtcd tfttatbdtcd  tcd  ta|||}td|t}t^t_tatbdtcd thttatbdtcd  tcd  ta|||}td|t}t^t_ttatbdtcd tbdtcd ta||| }td|t}t^t_ttatbdtcd tbdtcd ta||| }td|t}t^t_ttatbdtcd ta ta||}td|t}t^t_ttatbdtcd ta ta||}td|t}t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}td|t}t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}td|t}t^t_ttatbdtcd tbdtcd tcd ta||| }td|t}t^t_ttatbdtcd tbdtcd tcd ta||| }td|t}t^t_tatt ttatbdtcd tcd  ta||||}td|t}t^t_tatt ttatbdtcd tcd  ta||||}td|t}t^t_tattatbdtcd  ttatcd tbd	tcd  ta|||}td|t}t^t_tattatbdtcd  ttatcd tbd	tcd  ta|||}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta|||||	|}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta|||||	|}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta||||||}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta||||||}td|t}t^t_tattatbdtcd  ttatcd tbd	tcd  ta|||}td|t}t^t_tattatbdtcd  ttatcd tbd	tcd  ta|||}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta|||||	|}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta|||||	|}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta||||||}td|t}t^t_tatt ttatbdtcd  ttatcd tbd	tcd  ta||||||}td|t}t^t_tttatbdtcd tbdtcd ta||||}td|t}t^t_tatbdtcd tttatbdtcd  ta|||}td|t}t^t_ttcdtatbdtcd ta ta||}td|t}t^t_tatt tttatbdtcd  ta||||}td|t}t^t_tatt tttatbdtcd  ta|||||}td|t}t^t_tatbdtcd tttatbdtcd  ta||||}td|t}t^t_tatbdtcd ttttatbdtcd   ta|||||}td|t}t^t_tatbdtcd ttttatbdtcd   ta|||||}td|t}t^t_ttatbdtcd tbdtcd ta||| }td|t}t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}td|t}t^t_ttatbdtcd tbdtcd tcd ta||| }td|t}t^t_tatbdtcd ttatbdtcd tcd  ta||}td|t}t^t_tatbdtcd tttatbdtcd  tcd  ta|||}td|t}t^t_ttatbdtcd tbd	tcd tptatbdtcd tbdtcd  ta|||||}td|t}t^t_tatbdtcd ttatbdtcd tbd	tcd  tptatbdtcd tbdtcd  ta|||||}td|t}t^t_tatt ttatbdtcd tbd	tcd  tptatbdtcd tbdtcd  ta||||||}td|t}t^t_ttatbdtcd tbdtcd ta||| }td|t}t^t_ttatbdtcd ta ta||}td|t}t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}td|t}t^t_ttatbdtcd tbdtcd ta||| }td|t}t^t_ttatbdtcd tbdtcd ta||| }td|t}t^t_ttatbdtcd ta ta||}td|t}t^t_ttatbdtcd ta ta||}td|t}t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}td|t}t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}td|t}t^t_ttatbdtcd tbdtcd tcd ta||| }td|t}t^t_ttatbdtcd tbdtcd tcd ta||| }td|t}t^t_tatbdtcd ttatbdtcd tcd  ta||}td|tÃ}t^t_tatbdtcd ttatbdtcd tcd  ta||}td|tă}t^t_tatbdtcd tttatbdtcd  tcd  ta|||}td|tŃ} t^t_tatbdtcd tttatbdtcd  tcd  ta|||}td|tƃ}t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}td|tǃ}t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}td|tȃ}t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta|||||}td|tɃ}t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta|||||}	td|	tʃ}
t^t_tatt ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}td|t˃}t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}td|t̃}t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}td|t̓}t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}td|t΃}t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta|||||}td|tσ}t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta|||||}td|tЃ}t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}td|tу}t^t_tatt ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}td|t҃}t^t_ttatbdtcd tbdtcd ta||| }td|tԃ}t^t_ttatbdtcd tbdtcd ta||| }td|tփ}t^t_ttatbdtcd ta ta||}td|t׃} t^t_ttatbdtcd ta ta||}!td|!t؃}"t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}#td|#tك}$t^t_tatbdtcd ttatbdtcd tbdtcd  ta||||}%td|%tڃ}&t^t_ttatbdtcd tbdtcd tcd ta||| }'td|'tۃ}(t^t_ttatbdtcd tbdtcd tcd ta||| })td|)t܃}*t^t_tatbdtcd ttatbdtcd tcd  ta||}+td|+t݃},t^t_tatbdtcd ttatbdtcd tcd  ta||}-td|-tރ}.t^t_tatbdtcd tttatbdtcd  tcd  ta|||}/td|/t߃}0t^t_tatbdtcd tttatbdtcd  tcd  ta|||}1td|1t}2t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}3td|3t}4t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}5td|5t}6t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}7td|7t}8t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}9td|9t}:t^t_tatt ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||};td|;t}<t^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}=td|=t}>t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}?td|?t}@t^t_ttatbdtcd tbd	tcd ttatbdtcd tbdtcd  ta|||||}Atd|At}Bt^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta|||||}Ctd|Ct}Dt^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta|||||}Etd|Et}Ft^t_tatbdtcd ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}Gtd|Gt}Ht^t_tatt ttatbdtcd tbd	tcd  ttatbdtcd tbdtcd  ta||||||}Itd|It}Jt^t_tttatbdtcd tbdtcd ta||| }Ktd|Kt}Lt^t_tttta ta ta||| }Mtd|Mt}Nt^t_tatbdtcd tttta  ta||||}Otd|Ot}Pt^t_tatbdtcd ttttatbdtcd   ta|||||!|}Qtd|Qt}Rt^t_ttatbdtcd tbdtcd ta||| }Std|St}Tt^t_tatbdtcd ttatbdtcd tbdtcd  ta|||"|}Utd|Ut}Vt^t_tttatbdtcd tbdtcd ta||||}Wtd|Wt}Xt^t_tatbdtcd tttatbdtcd tbdtcd  ta||||"|}Ytd|Yt}Zt^t_tatbdtcd tttatbdtcd tbdtcd  ta||||"|}[td|[t}\t^t_ttatbdtcd tbdtcd tbd
tcd ttcdtatbdtcd tbdtcd  ta||||}]td|]t}^t^t_ttatbdtcd tbdtcd tbd
tcd ttcdtatbdtcd tbd	tcd  ta|||||#}_td|_t}`t^t_ttcdtatbdtcd tbdtcd ta||| }atd|at }bt^t_tttatbdtcd tbdtcd ta|||&|$|%}ctd|ct}dt^t_tatbdtcd ttcdtatbdtcd tbdtcd  ta|||"}etd|et}ft^t_tatbdtcd tttatbdtcd tbdtcd  ta|||&|$|%|"|}gtd|gt}ht^t_tatbdtcd tttatbdtcd tbdtcd  ta|||&|$|%|"|}itd|it}jt^t_tttatbdtcd tbdtcd tbdtcd tbdtcd ta|||)|*|'|(}ktd|kt}lt^t_tttatbdtcd tbdtcd tbdtcd tbdtcd ta|||)|*|'|+}mtd|mt}nt^t_tttatbdtcd tbdtcd tbdtcd tbd	tcd tatbdtcd tbdtcd  ta|||||-||)|,	}otd|ot	}pt^t_tttatbdtcd tbdtcd tbdtcd tbdtcd ta ta||||)|*|.}qtd|qt
}rt^t_tatbdtcd tttatbdtcd tbdtcd tbdtcd tbdtcd  ta||||)|*||'|(	}std|st}tt^t_tatbdtcd tttatbdtcd tbdtcd tbdtcd tbdtcd  ta||||)|*||'|+	}utd|ut}vt^t_tttatbdtcd tbdtcd tbdtcd tbdtcd ttatbdtcd tbd	tcd tbdtcd  ta ta||||||*|1|/|0
}wtd|wt}xt^t_tttatbdtcd tbdtcd tbdtcd tbd	tcd ta||||)|'|(}ytd|yt}zt^t_tatbdtcd tttatbdtcd tbdtcd tbdtcd tbd	tcd  ta|||||)|'|(|	}{td|{t}|t^t_ttttatbdtcd tbdtcd tbd	tcd  tbdtcd tbdtcd ta|3||||||)|2	}}td|}t}~t^t_tatbdtcd tbdtcd tbdtcd ttttatbdtcd tbdtcd tbd	tcd  tbdtcd tbdtcd  ta|3|||||-|4||)|"|}td|t}t^t_tttt ta||tt}td|t}t^t_tttt tt ta||5tt}td|t}t^t_ttatbdtcd tbdtcd tbd	tcd t ta||||6|7}td|t}t^t_ttatbdtcd tbdtcd tbd	tcd tbdtcd ta||||8}td|t}t^t_tatbdtcd tttatbdtcd  tbd	tcd tbdtcd  ta||||)|}td|t }t^t_ttat tbdtcd tbd	tcd tbdtcd ta||||)|9}td|t!}t^t_ttat tbdtcd tbd	tcd tbdtcd ta||||:}td|t"}t^t_ttat tbdtcd tbd	tcd tbdtcd ta|||)|;}td|t#}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd tbdtcd  ta|||||)||<}td|t$}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd tbdtcd  ta|||||)|=}td|t%}t^t_tatbdtcd ttatbdtcd tbd	tcd tbdtcd  ta||||>}td|t&}t^t_tatbdtcd ttat tbdtcd tbd	tcd tbdtcd  ta|||)|?|@|}td|t'}t^t_tcdt(ttatbdtcd tbdtcd tbdtcd   ta||||A}td|t)}t^t_ttatbdtcd tbdtcd t(ttatbdtcd tbdtcd tbdtcd   ta||||A}td|t*}t^t_ttatbdtcd tbdtcd tbd	tcd t t(ttatbdtcd tbdtcd tbdtcd   ta|||||6|B}td|t+}t^t_tcdt(ttatbdtcd tbdtcd tbdtcd  ttatbdtcd tbdtcd   ta||||A}td|t,}t^t_tcdt-ttatbdtcd tbdtcd tbd	tcd t(ttatbdtcd tbdtcd tbdtcd    ta|||||C}td|t.}t^t_tcdt-ttatbdtcd tbdtcd tbd	tcd t(ttatbdtcd tbdtcd tbdtcd    ta|||||D}td|t/}t^t_ttatbdtcd tbdtcd tbd	tcd t t(ttatbdtcd tbdtcd tbdtcd   ta|||||6|7}td|t0}t^t_ttatbdtcd tbdtcd tbd	tcd tbdtcd t(ttatbdtcd tbdtcd tbdtcd   ta|||||)|E}td|t1}t^t_tatbdtcd t(tttatbdtcd  tbdtcd   ta||||}td|t2}t^t_tatbdtcd tttatbdtcd  tbd	tcd tbdtcd  t(tttatbdtcd  tbdtcd   ta|||||)|}td|t3}t^t_tcdt(ttat tbdtcd tbdtcd   ta|||;}td|t4}t^t_ttatbd
tcd tbdtcd tbd	tcd tbdtcd t(ttatbd
tcd tbdtcd tbdtcd   ta|||||)|F}td|t5}t^t_ttatbd
tcd tbdtcd tbdtcd t(ttatbd
tcd tbdtcd tbdtcd   ta|||G|H}td|t6}t^t_ttatbd
tcd tbdtcd tbd	tcd t t(ttatbd
tcd tbdtcd tbdtcd   ta||||G|I|J}td|t7}t^t_ttatbd
tcd tbdtcd tbd	tcd t t(ttatbd
tcd tbdtcd tbdtcd   ta||||G|I|K}td|t8}t^t_ttatbd
tcd tbdtcd tbd	tcd tbdtcd t(ttatbd
tcd tbdtcd tbdtcd   ta||||L|(|M}td|t9}t^t_ttatbd
tcd tbdtcd tbd	tcd tbdtcd t(ttatbd
tcd tbdtcd tbdtcd   ta||||L|(|N}td|t:}t^t_ttat tbdtcd tbd	tcd tbdtcd t(ttat tbdtcd tbdtcd   ta||||)|;}td|t;}t^t_tatbdtcd t(ttatbdtcd tbdtcd   ta|||"|}td|t<}t^t_tcdtat(ttatbdtcd tbdtcd    ta|||O}td|t=}t^t_tatbdtcd t(ttatbdtcd tbdtcd   ta|||"|}td|t>}t^t_tatbdtcd t(ttatbdtcd tbdtcd   ta||||}td|Ðt?}t^t_tcdtat(ttatbd
tcd tbdtcd tbdtcd    ta||||P}td|Őt@}t^t_tatbdtcd t(ttat tbdtcd tbdtcd   ta|||?|@|}td|ǐtA}t^t_ttatbd
tcd tbdtcd tbd	tcd tbdtcd tat(ttatbd
tcd tbdtcd tbdtcd    ta|||||)|Q}td|ɐtB}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd tbdtcd  t(ttatbd
tcd tbdtcd tbdtcd   ta||||||)||R	}td|ːtC}t^t_tatbdtcd ttatbd
tcd tbdtcd tbdtcd  t(ttatbd
tcd tbdtcd tbdtcd   ta|||||S|T}td|͐tD}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd t  t(ttatbd
tcd tbdtcd tbdtcd   ta|||||||U|V|W
}td|ϐtE}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd t  t(ttatbd
tcd tbdtcd tbdtcd   ta|||||||U|V|X
}td|ѐtF}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd tbdtcd  t(ttatbd
tcd tbdtcd tbdtcd   ta||||||)||Y|Z
}td|ӐtG}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd tbdtcd  t(ttatbd
tcd tbdtcd tbdtcd   ta||||||)||Y|[
}td|ՐtH}t^t_tatbdtcd ttatbdtcd tbd	tcd tbdtcd  t(ttatbdtcd tbdtcd   ta|||||)|}td|אtI}t^t_tatbdtcd ttatbd
tcd tbdtcd tbd	tcd tbdtcd  t(ttatbd
tcd tbdtcd tbdtcd   ta||||)||?|@}td|ِtJ}t^t_tta|\}td|ېtK}g |^|`|b|d|f|h|j|l|n|p|r|t|v|x|z|||~|||||||||||||||||||||||||||||||||||đ|Ƒ|ȑ|ʑ|̑|Α|Б|ґ|ԑ|֑|ؑ|ڑ|ܑ|ޑ||||||||||||||||| |||||
||||||||||| |"|$|&|(|*|,|.|0|2|4|6|8|:|<|>|@|B|D|F|H|J|L|N|P|R|T|V|X|Z|\|^|`|b|d|f|h|j|l|n|p|r|t|v|x|z|||~|||||||||||||||||||||||||||||||||||đ|Ƒ|ȑ|ʑ|̑|Α|Б|ґ|ԑ|֑|ؑ|ڑ|ܑS )Nr   )]cons69cons2cons3cons68cons19cons1266cons8cons29cons20cons168cons1959cons1960cons96cons263cons1961cons1834cons64cons1962cons1963cons1964cons249cons1965cons1966cons1967cons1833cons4cons1257cons21cons1361cons1968cons1969cons170cons1970cons1971cons33cons1972cons1973cons1974cons802cons89cons90cons5cons52cons91cons385cons50cons1975cons1976cons1977cons54cons1978cons1101cons127cons1245cons13cons139cons1381cons1979cons1980cons198cons1981cons1982cons1983cons152cons465cons1767cons165cons950cons951cons1984cons1985cons805cons1986cons1987cons1988cons1989cons340cons1990cons1991cons1992cons1993cons1994cons1995cons40cons1996cons349cons1997cons1998cons1999cons2000cons2001cons2002cons2003b   am   dcnpqerf(L  Z sympy.integrals.rubi.constraintsr  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  r   r  r  x_r  r  r   replacement6742r  replacement6743r  replacement6744replacement6745replacement6746replacement6747replacement6748replacement6749replacement6750expreplacement6751replacement6752replacement6753m_replacement6754replacement6755replacement6756replacement6757replacement6758replacement6759replacement6760replacement6761replacement6762replacement6763replacement6764replacement6765replacement6766replacement6767replacement6768a_replacement6769replacement6770replacement6771r  replacement6772r  replacement6773replacement6774replacement6775replacement6776replacement6777replacement6778replacement6779replacement6780replacement6781r  replacement6782r  replacement6783replacement6784replacement6785replacement6786replacement6787replacement6788replacement6789replacement6790replacement6791replacement6792replacement6793r  n_replacement6794replacement6795replacement6796replacement6797replacement6798replacement6799replacement6800replacement6801r  replacement6802replacement6803replacement6804replacement6805replacement6806replacement6807replacement6808replacement6809r  replacement6810replacement6811replacement6812r  replacement6813r  replacement6814replacement6815replacement6816replacement6817replacement6818replacement6819replacement6820replacement6821replacement6822replacement6823replacement6824replacement6825replacement6826replacement6827replacement6828replacement6829replacement6830replacement6831replacement6832replacement6833replacement6834replacement6835replacement6836r  replacement6837r  replacement6838replacement6839replacement6840replacement6841replacement6842replacement6843replacement6844replacement6845replacement6846replacement6847replacement6848r  replacement6849r  replacement6850replacement6851replacement6852replacement6853replacement6854replacement6855replacement6856replacement6857replacement6858replacement6859replacement6860r  replacement6861b_replacement6862replacement6863With6864r  replacement6865replacement6866r  replacement6867replacement6868replacement6869replacement6870r  replacement6871r  replacement6872s_replacement6873replacement6874replacement6875replacement6876r  replacement6877replacement6878replacement6879replacement6880replacement6881replacement6882logreplacement6883replacement6884replacement6885F_replacement6886replacement6887u_v_r   With6888replacement6888w_With6889replacement6889r  p_replacement6890replacement6891replacement6892replacement6893replacement6894replacement6895replacement6896replacement6897replacement6898replacement6899d_replacement6900replacement6901replacement6902replacement6903r  replacement6904replacement6905replacement6906replacement6907replacement6908replacement6909replacement6910replacement6911replacement6912replacement6913replacement6914replacement6915replacement6916replacement6917replacement6918replacement6919replacement6920replacement6921replacement6922replacement6923replacement6924replacement6925replacement6926replacement6927replacement6928replacement6929replacement6930replacement6931replacement6932replacement6933(  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  Zpattern6742Zrule6742Zpattern6743Zrule6743Zpattern6744Zrule6744Zpattern6745Zrule6745Zpattern6746Zrule6746Zpattern6747Zrule6747Zpattern6748Zrule6748Zpattern6749Zrule6749Zpattern6750Zrule6750Zpattern6751Zrule6751Zpattern6752Zrule6752Zpattern6753Zrule6753Zpattern6754Zrule6754Zpattern6755Zrule6755Zpattern6756Zrule6756Zpattern6757Zrule6757Zpattern6758Zrule6758Zpattern6759Zrule6759Zpattern6760Zrule6760Zpattern6761Zrule6761Zpattern6762Zrule6762Zpattern6763Zrule6763Zpattern6764Zrule6764Zpattern6765Zrule6765Zpattern6766Zrule6766Zpattern6767Zrule6767Zpattern6768Zrule6768Zpattern6769Zrule6769Zpattern6770Zrule6770Zpattern6771Zrule6771Zpattern6772Zrule6772Zpattern6773Zrule6773Zpattern6774Zrule6774Zpattern6775Zrule6775Zpattern6776Zrule6776Zpattern6777Zrule6777Zpattern6778Zrule6778Zpattern6779Zrule6779Zpattern6780Zrule6780Zpattern6781Zrule6781Zpattern6782Zrule6782Zpattern6783Zrule6783Zpattern6784Zrule6784Zpattern6785Zrule6785Zpattern6786Zrule6786Zpattern6787Zrule6787Zpattern6788Zrule6788Zpattern6789Zrule6789Zpattern6790Zrule6790Zpattern6791Zrule6791Zpattern6792Zrule6792Zpattern6793Zrule6793Zpattern6794Zrule6794Zpattern6795Zrule6795Zpattern6796Zrule6796Zpattern6797Zrule6797Zpattern6798Zrule6798Zpattern6799Zrule6799Zpattern6800Zrule6800Zpattern6801Zrule6801Zpattern6802Zrule6802Zpattern6803Zrule6803Zpattern6804Zrule6804Zpattern6805Zrule6805Zpattern6806Zrule6806Zpattern6807Zrule6807Zpattern6808Zrule6808Zpattern6809Zrule6809Zpattern6810Zrule6810Zpattern6811Zrule6811Zpattern6812Zrule6812Zpattern6813Zrule6813Zpattern6814Zrule6814Zpattern6815Zrule6815Zpattern6816Zrule6816Zpattern6817Zrule6817Zpattern6818Zrule6818Zpattern6819Zrule6819Zpattern6820Zrule6820Zpattern6821Zrule6821Zpattern6822Zrule6822Zpattern6823Zrule6823Zpattern6824Zrule6824Zpattern6825Zrule6825Zpattern6826Zrule6826Zpattern6827Zrule6827Zpattern6828Zrule6828Zpattern6829Zrule6829Zpattern6830Zrule6830Zpattern6831Zrule6831Zpattern6832Zrule6832Zpattern6833Zrule6833Zpattern6834Zrule6834Zpattern6835Zrule6835Zpattern6836Zrule6836Zpattern6837Zrule6837Zpattern6838Zrule6838Zpattern6839Zrule6839Zpattern6840Zrule6840Zpattern6841Zrule6841Zpattern6842Zrule6842Zpattern6843Zrule6843Zpattern6844Zrule6844Zpattern6845Zrule6845Zpattern6846Zrule6846Zpattern6847Zrule6847Zpattern6848Zrule6848Zpattern6849Zrule6849Zpattern6850Zrule6850Zpattern6851Zrule6851Zpattern6852Zrule6852Zpattern6853Zrule6853Zpattern6854Zrule6854Zpattern6855Zrule6855Zpattern6856Zrule6856Zpattern6857Zrule6857Zpattern6858Zrule6858Zpattern6859Zrule6859Zpattern6860Zrule6860Zpattern6861Zrule6861Zpattern6862Zrule6862Zpattern6863Zrule6863Zpattern6864Zrule6864Zpattern6865Zrule6865Zpattern6866Zrule6866Zpattern6867Zrule6867Zpattern6868Zrule6868Zpattern6869Zrule6869Zpattern6870Zrule6870Zpattern6871Zrule6871Zpattern6872Zrule6872Zpattern6873Zrule6873Zpattern6874Zrule6874Zpattern6875Zrule6875Zpattern6876Zrule6876Zpattern6877Zrule6877Zpattern6878Zrule6878Zpattern6879Zrule6879Zpattern6880Zrule6880Zpattern6881Zrule6881Zpattern6882Zrule6882Zpattern6883Zrule6883Zpattern6884Zrule6884Zpattern6885Zrule6885Zpattern6886Zrule6886Zpattern6887Zrule6887Zpattern6888Zrule6888Zpattern6889Zrule6889Zpattern6890Zrule6890Zpattern6891Zrule6891Zpattern6892Zrule6892Zpattern6893Zrule6893Zpattern6894Zrule6894Zpattern6895Zrule6895Zpattern6896Zrule6896Zpattern6897Zrule6897Zpattern6898Zrule6898Zpattern6899Zrule6899Zpattern6900Zrule6900Zpattern6901Zrule6901Zpattern6902Zrule6902Zpattern6903Zrule6903Zpattern6904Zrule6904Zpattern6905Zrule6905Zpattern6906Zrule6906Zpattern6907Zrule6907Zpattern6908Zrule6908Zpattern6909Zrule6909Zpattern6910Zrule6910Zpattern6911Zrule6911Zpattern6912Zrule6912Zpattern6913Zrule6913Zpattern6914Zrule6914Zpattern6915Zrule6915Zpattern6916Zrule6916Zpattern6917Zrule6917Zpattern6918Zrule6918Zpattern6919Zrule6919Zpattern6920Zrule6920Zpattern6921Zrule6921Zpattern6922Zrule6922Zpattern6923Zrule6923Zpattern6924Zrule6924Zpattern6925Zrule6925Zpattern6926Zrule6926Zpattern6927Zrule6927Zpattern6928Zrule6928Zpattern6929Zrule6929Zpattern6930Zrule6930Zpattern6931Zrule6931Zpattern6932Zrule6932Zpattern6933Zrule6933r  r  r  special_functions   s  ~ 4
4
4
(
(
(
H
H
H
h
h
h
n
n
n
T
T
T
n
n
n
<
<
<
B
B
B
D
D
D
4
4
(
(
H
H
<
<
8
8
H
H
R
R
R
R
H
H
R
R
R
R
8
:
.
2
4
<
B
B
4
H
<
>
D
\
n
f
4
(
H
4
4
(
(
H
H
<
<
>
>
DF^^pphr^^pprh66**JJ>>@@FF^^rrhr^^pprh8$4F6J:NNpr<>NTT\\`rr\rt.:PV`NLLnlZbVt|VJ~RJRRZX   rU  c                 C   sR   t t| ||  td  tt|  |t | ||  t| ||   | | S Nr|  )r  r  r  r  Pir  rz  rx  xr  r  r  r       Rr  c                 C   sT   t t| ||  td  tt|  | t | ||  t| ||   | | S rV  )r  r  r  r  rW  r  rX  r  r  r  r    s   Tr  c                 C   sR   t t| ||  td tt|  | t | ||  t| ||   | | S rV  )r  r  r  r  rW  r  rX  r  r  r  r    rZ  r  c              	   C   sl   t td|  | tttdd tdd ttdd tdd | td  |td   tt |S Nr|  ry     r  r  r  r   r  rW  rx  rY  r  r  r  r    s   lr  c                 C   s&   t t| | | | tt|| S N)r   r  r  r  r^  r  r  r  r       &r  c              	   C   sj   t td|  | tttdd tdd ttdd tdd | td |td   tt |S r[  r]  r^  r  r  r  r       jr  c                 C   s   t td| tt|td   t||td  t| ||  td   || t||td  t| ||   |td  | S Nr|  ry  )r  r  r  rW  r   r  r  r  rz  rx  r{  rY  r  r  r  r    s   r  c                 C   s   t td| tt|td   t||td  t| ||  td   ||t||td  t| ||   |td  | S rb  )r  r  r  rW  r   r  r  r  rc  r  r  r  r       r  c                 C   s   t td| tt|td   t||td  t| ||  td  || t||td  t| ||   |td  | S rb  )r  r  r  rW  r   r  r  r  rc  r  r  r  r    rd  r  c              	   C   s   t |tt|  tt| td  td|  | |  | |td |td |   || tt| ||  t|||td    td|  | S rV  )r  r  rW  r   r  r  r  r  rz  rx  r~  r}  rY  r  r  r  r       r  c              	   C   s   t |tt|  tt| td  td|  | |  | |td |td |   ||tt| ||  t|||td    td|  | S rV  )r  r  rW  r   r  r  r  r  re  r  r  r  r       r  c              	   C   s   t |tt|  tt| td td|  | |  | |td |td |   || tt| ||  t|||td    td|  | S rV  )r  r  rW  r   r  r  r  r  re  r  r  r  r    rg  r  c                 C   s  t |td td|  t||td  t| ||   t|||td    || t |tt|  t||td  t| td  td|  | |  | |td |td |    || t||td  t| ||   t|||td    td|  | S Nr|  r  r  r   r  r  r  rW  r  rz  rx  r~  r}  r{  rY  r  r  r  r        r  c                 C   s  t |td td|  t||td  t| ||   t|||td    || t |tt|  t||td  t| td  td|  | |  | |td |td |    || t||td  t| ||   t|||td    td|  | S rh  r  r  r   r  r  r  rW  r  rl  r  r  r  r    rm  r  c                 C   s  t |td td|  t||td  t| ||   t|||td    || t |tt|  t||td  t| td td|  | |  | |td |td |    || t||td  t| ||   t|||td    td|  | S rh  r  r  r   r  r  r  rW  r  rl  r  r  r  r        r  c              	   C   f   t td|  | tttdd tdttdd tdd ||td   t| tt |S r[  r  r  r  r   r  r  rW  rx  r~  r}  rY  r  r  r  r       fr  c              	   C   sP   t t|||td   | |t t| | t|||td    | | S rV  )r   r  r  r  rs  r  r  r  r       Pr  c              	   C   rq  r[  rr  rs  r  r  r  r    rt  r  c                 C   s&  t td| |td  t||td  t| ||   t|||td    || t td| tt|td   t||td  t| td  td|  | |  | |td |td |    || t||td  t| ||   t|||td    |td  | S rb  rk  rl  r  r  r  r       ( r  c                 C   s&  t td| |td  t||td  t| ||   t|||td    || t td| tt|td   t||td  t| td  td|  | |  | |td |td |    || t||td  t| ||   t|||td    |td  | S rb  rn  rl  r  r  r  r    rv  r  c                 C   s$  t td| |td  t||td  t| ||   t|||td    || t td| tt|td   t||td  t| td td|  | |  | |td |td |    || t||td  t| ||   t|||td    |td  | S rb  ro  rl  r  r  r  r  #  s   & r  c                 C   s   t tdtt t| ||  t| ||   t| ||  td   || t| ||  t| ||  td  | | S N   r|  r  r  r  rW  r   r  r  r  rX  r  r  r  r  '     r  c                 C   s~   t tdtt t| ||  t| ||   t| ||  td   ||t| ||  t| ||  td  | | S rw  r  r  r  rW  r   r  r  r  rX  r  r  r  r  +     ~r  c                 C   s~   t tdtt t| ||  t| ||   t| ||  td  || t| ||  t| ||  td  | | S rw  r  r  r  rW  r   r  r  r  rX  r  r  r  r  /  r|  r  c              	   C   s   t td|  tt|td   t||td  t| |  t| td  |td   || t||td  t| | td  |td  | S Nrx  ry  r|  ry  rx  r{  rY  r  r  r  r  3  rf  r  c              	   C   s   t td|  tt|td   t||td  t| |  t| td  |td   ||t||td  t| | td  |td  | S r~  r{  r  r  r  r  r  7  rg  r  c              	   C   s   t td|  tt|td   t||td  t| |  t| td |td   || t||td  t| | td  |td  | S r~  r}  r  r  r  r  r  ;  rg  r  c                 C   L   t td| tt|  | ||  | t|td  ||| ||  |S Nry  r|  )r  r  r+   r   r  rc  r  r  r  r  ?     Lr  c                 C   r  r  )r  r  r+   r   r  rc  r  r  r  r  C  r  r  c                 C   r  r  )r  r  r+   r   r  rc  r  r  r  r  G  r  r  c                 C   sX   t tt| ||  td  td t|  |t | ||  t| ||   | | S rV  )r  r  rW  r  r  rX  r  r  r  r  K     Xr  c                 C   sZ   t tt| ||  td  td t|  | t | ||  t| ||   | | S rV  )r  r  rW  r  r  rX  r  r  r  r  O     Zr  c              
   C   s   t t|  | tttdd tdd ttdd tdd t t | td  |td  td  td |t t|  | tttdd tdd ttdd tdd tt | td  |td  td  td | S Nry  r|  r\  )r  r  r  r   r  rW  r^  r  r  r  r  S  s   r  c              
   C   s   t | | tttdd tdd ttdd tdd t t | td  |td  td  td |t | | tttdd tdd ttdd tdd tt | td  |td  td  td | S r  )r  r  r   r  r  rW  r^  r  r  r  r  W  s   r  c              	   C      t ||td  t||td  tt| ||  td  td  || t||td  t| ||   |td  | S r  )r  r  r   r  rW  r  r  rc  r  r  r  r  [     r  c              	   C   r  r  )r  r  r   r  rW  r  r  rc  r  r  r  r  _  r  r  c              	   C      t tdt| ||  t| ||   tt| ||  td  td  || t| ||  t| ||  td  | | S rV  r  r  r   r  r  rW  r  rX  r  r  r  r  c  r  r  c              	   C   r  rV  r  r  r   r  r  rW  r  rX  r  r  r  r  g  r  r  c              	   C      t td|  |td  t||td  t| |  tt| td  |td  td  || t||td  t| | td  |td  | S rb  r  r  r  r  r  r  k     r  c              	   C   r  rb  r  r  r  r  r  r  o  r  r  c                 C   s   t tdtdt |   ttt| td  |td  ||tt| | tt| td  |td  td  t| td   | S r  )r  r  rW  r   r  r  r  r  rx  r~  rY  r  r  r  r  s  s   r  c                 C   s   t tdtdt |   ttt| td  |td  || tt| | tt| td  |td  td  t| td   | S r  )r  r  rW  r   r  r  r  r  r  r  r  r  w  s   r  c              
   C   s  t tdtdt |   t||td  tt| td  |td   ||t |td t| td   t||td  t| |  tt| td  |td  td  || t||td  t| |  tt| td  |td  td  t| td   | S Nry  r|  ri  rj  )r  r  rW  r   r  r  r  r  rx  r~  r{  rY  r  r  r  r  {  rm  r  c              
   C   s  t tdtdt |   t||td  tt| td  |td   || t |td t| td   t||td  t| |  tt| td  |td  td  || t||td  t| |  tt| td  |td  td  t| td   | S r  )r  r  rW  r   r  r  r  r  r  r  r  r    s    r  c              
   C   sL  t | td| td  t||td  tt| td  |td   ||t t| td  |td  t||td  t| |  tt| td  |td  td  || t| ||td   td|td  |td   | t||td  t| |  tt| td  |td  td  |td  | S rb  )r  r  r   r  rW  r  r  r  r  r  r  r  r    s   N r  c              
   C   sN  t | td| td  t||td  tt| td  |td   || t t| td  |td  t||td  t| |  tt| td  |td  td  || t| ||td   td|td  |td   | t||td  t| |  tt| td  |td  td  |td  | S rb  )r  r  r   r  rW  r  r  r  r  r  r  r  r    s   P r  c                 C   s   t tdtdt |   ttt| td  |td  ||t|tdt |   | tt| | tt| td  |td  td  t| td   | S r  )r  r  rW  r   r  r  r  r  r  r  r  r  r       r  c                 C   s   t tdtdt |   ttt| td  |td  ||t|tdt |   | tt| | tt| td  |td  td  t| td   | S r  )r  r  rW  r   r  r  r  r  r  r  r  r    r  r  c              
   C   s8  t tdtdt |   t||td  tt| td  |td   ||t |td t| td   t||td  t| |  tt| td  |td  td  || t|| tdt |  |  | t||td  t| |  tt| td  |td  td  t| td   | S r  )r  r  rW  r   r  r  r  r  r  r  r  r  r       : r  c              
   C   s8  t tdtdt |   t||td  tt| td  |td   ||t |td t| td   t||td  t| |  tt| td  |td  td  || t|| tdt |  |  | t||td  t| |  tt| td  |td  td  t| td   | S r  )r  r  rW  r   r  r  r  r  r  r  r  r    r  r  c              
   C   s  t | td| td  t||td  tt| td  |td   || t t| td  |td  t||td  t| |  tt| td  |td  td  || t||td  t| |  tt| td  |td  td  |td  | S rb  )r  r  r   r  rW  r  r  r  r  r  r  r  r    rp  r  c              
   C   s  t | td| td  t||td  tt| td  |td   || t t| td  |td  t||td  t| |  tt| td  |td  td  || t||td  t| |  tt| td  |td  td  |td  | S rb  )r  r  r   r  rW  r  r  r  r  r  r  r  r    rp  r  c                 C   s&   t t|td | ||  | | S Nry  )r  r  r  rz  rx  r  rY  r  r  r  r    r`  r  c                 C   s`   t ||  t||td  t|td | |  ||t|| t|td | |  |  | S Nri  ry  r  r   r  r  r  rx  r{  r  rY  r  r  r  r       `r  c              
   C   s~   t tt| | t | | tttdtdtdttdtdtd|  |  | t t| | td td | S r  r  r  r  r  r   r  r^  r  r  r  r    r|  r  c                 C   sp   t | |td  t||td  t|td | |  ||t||td  t|| |  |td  | S Nry  ri  r  r  r   r  r  r  r  r  r  r    s   pr  c              	   C   s   t ||td  tt|td |td t|td |td |  |  |td td  | t || | | |   t|td  t| |  | S r  )r  r  r  r   r  r  r  r  r  r  r       r  c                 C   s\   t ||td  t| | |  ||  | t ||td  t|| |  ||  | S r  )r  r  r  r  r  r  r  r    s   \r  c              	   C   sh   t || t||td  t|td | ||   ||t|| t|td | ||   | | S r  r  rz  rx  r{  r  rY  r  r  r  r       hr  c              	   C   sx   t ||td  t||td  t|td | ||   ||t||td  t|| ||   |td  | S r  r  r  r  r  r  r    s   xr  c                 C   B   t t| ||  | | t | ||  t| ||   | | S r_  )r  r  r  rX  r  r  r  r       Br  c                 C   z   t ||td  t||td  t| ||   | ||   || t||td  t| ||   |td  | S r  )r  r  r   r  r  r  rc  r  r  r  r       zr  c                 C   b   t tdtt| ||  t| ||   || t| ||  t| ||  td  | | S rV  r  r  r   r  r  r  rX  r  r  r  r       br  c                 C   v   t td|td  t|| t| |  t| |  || t||td  t| | td  |td  | S rb  r  r  r  r  r  r       vr  c              	   C     t | | ||td   t||td  t| ||  td  || t td|td  t|| t| ||   t| ||   || t||td  t| ||  td  |td  | t| ||  t| ||  td  ||td   | S Nry  ri  r|  r  rc  r  r  r  r        r  c                 C   sb   t || tt| | |||   |||   || tt|||  t| ||   | | S r_  )r  r   r  r  r  re  r  r  r  r    r  r  c              	   C   s   t || t|| t| | |||    |||   || t || t||td  t|||   t| ||   || t|| t|||   t| ||   | | S Nri  )r  r   r  r  r  r  rl  r  r  r  r    s   r  c              
   C   s   t ||td  t||td  t|||   t| ||   || t ||td  t||td  t| | |||    |||   || t||td  t|||   t| ||   |td  | S r  r  rl  r  r  r  r    s   r  c                 C   sN   t ttdt| ||   | | t | ||  t| ||   | | S rV  )r  r  r  r  r  rX  r  r  r  r       Nr  c                 C   s.   t | | | t t| | t| |  | S r_  )r  r  r  r^  r  r  r  r    s   .r  c                 C   sn   t ||td  t||td  t| ||   || t||td  t| ||   |td  | S r  )r  r  r   r  r  r  rc  r  r  r  r       nr  c                 C   s@   t t| ||  | |t | ||  t| ||   | | S r_  )r  r  r  rX  r  r  r  r    s   @r  c                 C   r  r_  )r  r  r  rX  r  r  r  r    r  r  c              
   C   s   t | | tttdtdtdttdtdtdt |  |  td |t | | tttdtdtdttdtdtdt|  |  td | S r  )r  r  r   r  r  r^  r  r  r  r    r  r  c              
   C   s   t tt| |t t|  | tttdtdtdttdtdtdt |  |  td | t t|  | tttdtdtdttdtdtdt|  |  td | t t| | td td | S r  )r  r  r  r  r  r   r  r^  r  r  r  r       r  c                 C   r  r  )r  r  r   r  r  r  rc  r  r  r  r    r  r  c                 C   r  r  )r  r  r   r  r  r  rc  r  r  r  r    r  r  c                 C   r  rV  r  r  r   r  r  r  rX  r  r  r  r    r  r  c                 C   r  rV  r  r  r   r  r  r  rX  r  r  r  r    r  r  c                 C   r  rb  r  r  r  r  r  r    r  r  c                 C   r  rb  r  r  r  r  r  r    r  r  c              	   C   r  r  r  rc  r  r  r  r    r  r  c              	   C   r  r  r  rc  r  r  r  r    r  r  c                 C   sh   t || tt|||  t| ||   |||   ||tt|||  t| ||   | | S r_  )r  r   r  r  r  r  re  r  r  r  r    r  r  c                 C   j   t || tt| ||  t|||   |||   || tt|||  t| ||   | | S r_  )r  r   r  r  r  r  re  r  r  r  r  #  ra  r  c              	   C   s   t || t|| t|||   t| ||   |||   ||t || t||td  t|||   t| ||   || t|| t|||   t| ||   | | S r  )r  r   r  r  r  r  r  rl  r  r  r  r  '     r  c              	   C      t || t|| t| ||   t|||   |||   || t || t||td  t|||   t| ||   || t|| t|||   t| ||   | | S r  )r  r   r  r  r  r  r  rl  r  r  r  r  +     r  c              	   C      t ||td  t||td  t|||   t| ||   || t ||td  t||td  t| ||   t|||   |||   || t||td  t|||   t| ||   |td  | S r  )r  r  r   r  r  r  r  rl  r  r  r  r  /     r  c              	   C   s   t ||td  t||td  t|||   t| ||   ||t ||td  t||td  t| ||   t|||   |||   || t||td  t|||   t| ||   |td  | S r  )r  r  r   r  r  r  r  rl  r  r  r  r  3  r  r  c                 C   j   t || tt| ||  t|||   |||   || tt|||  t| ||   | | S r_  )r  r   r  r  r  re  r  r  r  r  7  ra  r  c                 C   sh   t || tt| ||  t|||   |||   ||tt|||  t| ||   | | S r_  )r  r   r  r  r  re  r  r  r  r  ;  r  r  c              	   C      t || t|| t| ||   t|||   |||   || t || t||td  t|||   t| ||   || t|| t|||   t| ||   | | S r  )r  r   r  r  r  r  rl  r  r  r  r  ?  r  r  c              	   C   s   t || t|| t| ||   t|||   |||   ||t || t||td  t|||   t| ||   || t|| t|||   t| ||   | | S r  )r  r   r  r  r  r  rl  r  r  r  r  C  r  r  c              	   C   s   t ||td  t||td  t|||   t| ||   ||t ||td  t||td  t|||   t| ||   |||   || t||td  t|||   t| ||   |td  | S r  )r  r  r   r  r  r  r  rl  r  r  r  r  G  r  r  c              	   C      t ||td  t||td  t|||   t| ||   || t ||td  t||td  t| ||   t|||   |||   || t||td  t|||   t| ||   |td  | S r  )r  r  r   r  r  r  r  rl  r  r  r  r  K  r  r  c                 C   r  r_  )r  r  r  rX  r  r  r  r  O  r  r  c                 C   r  r_  )r  r  r  rX  r  r  r  r  S  r  r  c              
   C   s   t | | tttdtdtdttdtdtd|  |  td |t | | tttdtdtdttdtdtd| |  td | S r  )r  r  r   r  r^  r  r  r  r  W  r  r  c              
   C   s   t tt| |t | | tttdtdtdttdtdtd|  |  td | t | | tttdtdtdttdtdtd| |  td | t t| | td td | S r  r  r^  r  r  r  r  [  s   r  c                 C   r  r  )r  r  r   r  r  r  rc  r  r  r  r  _  r  r  c                 C   r  r  )r  r  r   r  r  r  rc  r  r  r  r  c  r  r  c                 C   r  rV  r  r  r   r  r  r  rX  r  r  r  r  g  r  r  c                 C   r  rV  r  r  r   r  r  r  rX  r  r  r  r  k  r  r  c                 C   r  rb  r  r  r  r  r  r  o  r  r  c                 C   r  rb  r  r  r  r  r  r  s  r  r  c              	   C   r  r  r  rc  r  r  r  r  w  r  r  c              	   C   r  r  r  rc  r  r  r  r  {  r  r  c                 C   sj   t || tt|||  t| ||   |||   || tt|||  t| ||   | | S r_  )r  r   r  r  r  r  re  r  r  r  r    ra  r  c                 C   r  r_  )r  r   r  r  r  r  re  r  r  r  r    ra  r  c              	   C   s   t || t|| t|||   t| ||   |||   || t || t||td  t|||   t| ||   || t|| t|||   t| ||   | | S r  )r  r   r  r  r  r  r  rl  r  r  r  r    r  r  c              	   C   r  r  )r  r   r  r  r  r  r  rl  r  r  r  r    r  r  c              	   C   r  r  )r  r  r   r  r  r  r  rl  r  r  r  r    r  r  c              	   C   r  r  )r  r  r   r  r  r  r  rl  r  r  r  r    r  r  c                 C   r  r_  )r  r   r  r  r  re  r  r  r  r    ra  r  c                 C   r  r_  )r  r   r  r  r  re  r  r  r  r    ra  r  c              	   C   r  r  )r  r   r  r  r  r  rl  r  r  r  r    r  r  c              	   C   r  r  )r  r   r  r  r  r  rl  r  r  r  r    r  r  c              	   C   s   t ||td  t||td  t|||   t| ||   || t ||td  t||td  t|||   t| ||   |||   || t||td  t|||   t| ||   |td  | S r  )r  r  r   r  r  r  r  rl  r  r  r  r    r  r  c              	   C   r  r  )r  r  r   r  r  r  r  rl  r  r  r  r     r  r   c                 C   sN   t t|td | ||  | | t | ||  t|| ||   | | S r  )r  r  r  r  r  r  r  r    r  r  c              
   C   sb   t t|t| |t | | | tt||t|td |td |  |  |td  | S r  )r  r  r  r  r   r  )rx  r  rY  r  r  r  r    r  r  c                 C   sv   t ||td  t|| |  |td  |t || | | |   t|| td | |  | |td   | S r  )r  r  r  r  r  r  r  r    r  r  c                 C   s   d}t ||td  t||td  | ||  |td   t|  ||   ||t||td  t|| ||   |td  | S )NTry  ri  )r  r  r   r  r  r  )rz  rx  r{  r  rY  	_UseGammar  r  r  r    s   r  c                 C   s    t ttd| ||  | |S )Nrj  r  r  r  rX  r  r  r  r    s    r  c              	   C   sb   t || t||td  ttd| ||   || t|| ttd| ||   | | S )Nri  rj  r  r   r  r  r  rc  r  r  r  r    r  r  c                 C   s$   t t|td | ||  | |S r  r  r  r  r  r  r       $r  c              	   C   sj   t || t||td  t|td | ||   || t|| t|td | ||   | | S r  r  r  r  r  r  r	    ra  r	  c              	   C   sz   t ||td  t||td  t|td | ||   || t||td  t|| ||   |td  | S r  )r  r  r   r  r  r  r  r  r  r
    r  r
  c                 C   s"   t t| ||  | ||  |S r_  )r  r  r  r  r  r  r       "r  c                 C   s"   t t| ||  | ||  |S r_  )r  r  )rz  rx  r~  r  rY  r  r  r  r    r  r  c                 C   s   t ttd| ||  |S r  r   r  r  rX  r  r  r  r    s   r  c                 C   s2   t t|td | ||  ||td   | S r  )r  r  r  )rz  rx  srY  r  r  r  r       2r  c                 C   s$   t || ttd| ||   |S r  r  rc  r  r  r  r    r  r  c              	   C   s   t |||td   t||td  t|td | ||   ||t|| t|td | ||   ||td   | S r  r  r  r   r  r  rz  rx  r{  r  rY  r  r  r  r    rz  r  c              	   C   s|   t || |td  t||td  t|td | ||   ||t||td  t|| ||   |td  | S r  r  r  r  r  r  r    s   |r  c              	   C   sZ   t || tt|td | |||  |  || t|t|| |||  |   | S r  r  r   r  r  r  rz  rx  r  r  r  rY  r  r  r  r    r  r  c              	   C   sr   t td||  tt|td | |||  |  || t|t|td | |||  |   ||  | S r  r  r  r   r  r  r  r  r  r  r    s   rr  c                 C   s0   t t|td || ||  |  ||  |S r  r  r  r  )rz  rx  r~  r}  r  r  r  rY  r  r  r  r       0r  c                 C   s0   t t|td | |||  |  ||  |S r  r  r  r  r  r  r    r  r  c              
   C   s   t || |td  t|| t|td | |||  |   || t||td  t|| |||  |   |td  | S r  r  rz  rx  r{  r  r  r  rY  r  r  r  r     rd  r  c              
   C   s   t |td ||  t|| t|td | |||  |   || t||td  t|td | |||  |   ||  | S r  r  r  r  r  r  r       r  c	           	   	   C   s   t || ||  tt|td | |||  |  t|||  |td   | || tt|td | |||  |  t|||  |  ||  | S r  )r  r   r  r  r  r  )	rz  rx  r~  r{  r  r  r  r  rY  r  r  r  r    r  r  c              
   C   s   t |tt|td || ||  |  || t | | tt|td || ||  |  | ||   || t|t||| ||  |   | S r  r  )rz  rx  r~  r  r  rY  r  r  r  r       r  c              
   C   s   t || |td  t||td  t|td || ||  |   | ||   || t||td  t||| ||  |   |td  | S r  r  )rz  rx  r~  r{  r  r  rY  r  r  r  r    rg  r  c              	   C   sD   t t|td || ||||    |  || | t|   |S r  )r  r  r  r  )Frz  rx  r~  r}  r  r  rY  r  r  r  r       Dr  c                 C   s   t || || |	 t|   t|||
  |td  t|td || ||||
    |	   |
|
 t|||
  | t|td || ||||
    |	   || |	 t|   |
 S r  )r  r  r   r  r  r  )r  rz  rx  r~  r}  r  r  r{  r  r  rY  r  r  r  r    s   r  c              	   C   s\   t |ttttfrdS zt||| |}tt|}W n tt	fy'   Y dS w |r,dS dS NFT

isinstanceintr  floatr  r  r6   r   	TypeErrorAttributeError)r  uvrY  wresr  r  r  r"       r"  c                 C   s,   t ||| |}t|t| td | |S r  )r  r  r  r  )r  r  r  rY  r  r  r  r  r#  )  s   r#  c              	   C   s\   t |ttttfrdS zt||| |}tt|}W n tt	fy'   Y dS w |r,dS dS r  r  )r  r  r  r  rY  zr  r  r  r  r%  /  r  r%  c                 C   sf   t ||| |}tt|t|| t| td | | || t|t| td | t| | S r  )r  r   r-  r  r  r  r  r  )r  r  r  r  rY  r  r  r  r  r&  <  s   Vr&  c                 C   s   t |||td   t|t| ||   |td  t| ||  td  ||t|t| ||   | | ||   ||td   | S r  r  r  r   r  r  rz  rx  r~  r  rY  r  r  r  r(  B     r(  c                 C   sn   t |t|t| ||   | t| ||  td  || t|t| ||   | | ||   | | S r  r  r   r  r  r  r  r  r  r  r)  F  r  r)  c              	   C   sP   t td| ttt|t| | |  | ||  | |||| ||  |S r  r  r  r+   r   r   r  )rz  rx  r~  r{  r  rY  r  r  r  r*  J  ru  r*  c                 C   sf   t || t|t| ||   | t| ||  td  || t||t| ||   |  | S r  r  rz  r~  r  r  rY  r  r  r  r+  N  rt  r+  c                 C   s   t || ||| td   t|t| ||   |td  t| ||  td  ||t||t| ||   |  || td  | S r  r  r  r  r  r  r,  R  r  r,  c                 C   s>   t t|t| ||    | |td  ||td|  S rb  r+   r   r  r  r  r  r  r  r-  V  s   >r-  c              	   C   s   t || |td  t|| |t| ||   |  t| ||  td  || t||td  |t| ||   |  |td  | S r  r  rz  r~  r{  r  r  rY  r  r  r  r.  Z     r.  c              	   C   s   t || ||||  td   t|| |t| ||   |td   t| ||  td  ||t||td  |t| ||   |  |||  td  | S r  r  r  r  r  r  r/  ^  s   r/  c                 C   s   t td| t|| |t| |  |td   t| | td  ||t|| |t| |  |  t| | td  | S r  )r  r  r   r  )rz  r~  r{  r  rY  r  r  r  r0  b  s   r0  c                 C   sD   t t|| td  |t| ||    |  ||td|  S Nrj  ry  r+   r   r  r  r  r  r  r  r1  f  r  r1  c                 C   s*   t | ||  || t| ||    |S r_  r  r  rz  rx  r}  rY  r  r  r  r3  j     *r3  c                 C   s6   t td|t| ||   |  | t|| | S r  )r   r  r  r  r  r  r  r  r4  n  s   6r4  c              	   C   s   t || t|t| ||   |td  |t| ||   |  || t||t| ||   |td   | ||   ||  | S r  r  rz  rx  r~  r}  r  rY  r  r  r  r5  r  r  r5  c                 C   s"   t tt| ||  ||  |S r_  r  r  r  r  r  r  r  r6  v  r  r6  c                 C   sN   t tt|t| ||   t|td tt| td || |  |S rV  )r  r  r  r  r  r  rW  re  r  r  r  r7  z  r  r7  c                 C   sR   t tt|t| ||   t| td tt | td || |  |S rV  )r  r  r  r  r  r  rW  re  r  r  r  r8  ~  rZ  r8  c              	   C   s   t td||td   t|t| ||   |td  |t| ||   |  || t|t| ||   | | ||   || |td   | S r  r  r  r  r  r  r9    rg  r9  c                 C   s^   t t| ||   |  |t| ||   |  t|td t| ||    ||  |S r  )r  r  r  r  r  r  r  r  r:       ^r:  c              	   C   sX   t td| ttttd|t| |  |  | ||  | |||| ||  |S r  r  )rz  rx  r}  r{  rY  r  r  r  r;    r  r;  c              	   C   s`   t td| ttt|t| | |t| |  |  | ||  | |||| ||  |S r  r  )rz  rx  r~  r}  r{  r  rY  r  r  r  r<    r  r<  c              	   C   sF   t ttd|td |t| ||    |   ||td|  S r  r  rz  r}  r  rY  r  r  r  r=    s   Fr=  c                 C   s2   t || |t| ||   |td   | |S r  )r  r  r  rz  r~  r}  r  r  rY  r  r  r  r>    r  r>  c                 C   s0   t | | t| t| ||    ||  |S r_  r  )rz  r}  r  r  rY  r  r  r  r?    r  r?  c              	   C   sv   t | td |  |td |   tt|t| ||   t|| td  tt| | td ||  |S r  r  r  r  r  r  r  rW  r  r  r  r  r@    r  r@  c              	   C   sz   t | td |  |td |   tt|t| ||   t| | td  tt | | td ||  |S r  r  r  r  r  r  r  rW  r  r  r  r  rA    r  rA  c              	   C   s   t |||td  td  t|t| ||   |td  |t| ||   |  || t|| |t| ||   |td   | | S r  r  r  r  r  r  rB    r  rB  c              	   C   s   t td||| td   t|t| ||   |td  |t| ||   |  || t||t| ||   |  ||| td   | S r  r  r  r  r  r  rC    r  rC  c              	   C   sX   t t|t| ||    | |td |t| ||    |   ||td|  S rb  r  r  r  r  r  rD    r  rD  c                 C   sv   t ||td  t|| |t| |  | t| |   || t||td  ||td  t| |   | S r  r  rz  r}  r{  rY  r  r  r  rE    r  rE  c                 C   s   t tt| | | |S r_  r  r  r  )rz  r}  rY  r  r  r  rF    s   rF  c                 C   sV   t || t| |  |t| |  |  | t||td  ||td   | S r  )r   r  r  r  r  r  r  r  rG    s   VrG  c                 C   s   t || |td  t| |  |   t|td |td  t| |   t| t| |   | | |td   |S r  )r  r  r  r  r  r  r  r  r  rH    rz  rH  c                 C   s"   t tt| ||  ||  |S r_  r  r  r  r  r  rI    r  rI  c                 C   sD   t t|| td  |t| ||    |  ||td|  S r  r  )rz  r}  r{  r  rY  r  r  r  rJ    r  rJ  c                 C   s*   t |t| ||   | || |  |S r_  r  r  r  r  r  rK    r  rK  c                 C   sJ   t |||td   |t| ||   |td   ||td   |S r  )r  r  r  rz  r~  r}  r{  r  r  rY  r  r  r  rL    s   JrL  c                 C   s0   t | | t| t| ||    ||  |S r_  r  )rz  r}  r{  r  r  rY  r  r  r  rM    r  rM  c              	   C   s   t | |tdd   ||tdd    tt|t| ||   t||tdd   td  tt| |tdd   td ||  |S Nri  r|  r  r  r  r  r  rN    r  rN  c              	   C   s   t | |tdd   ||tdd    tt|t| ||   t| |tdd   td  tt | |tdd   td ||  |S r  r  r  r  r  r  rO    r  rO  c              	   C   s   t ||||td   td  |td  t|| |t| ||   |td   |t| ||   |  || t|||td   |t| ||   |td   ||td   | S r  r  r  r  r  r  rP    s   rP  c              	   C   s   t |td ||||  td   t|| |t| ||   |td   |t| ||   |  || t||td  |t| ||   |  ||||  td   | S r  r  r  r  r  r  rQ    s   rQ  c                 C   s   t || |t| |  |  |td  t| |  | |   t|| td |td  t| |   t| t| |   | | |td   |S r  )r  r  r  r  r  )rz  r~  r}  r{  r  rY  r  r  r  rR    rf  rR  c                 C   s^   t t|| td  |t| ||    |  |t| ||    |  ||td|  S r  r  r  r  r  r  rS    r  rS  c                 C   s<   t tt|td tt|| | t| |||t|S r  )r+   r   r-  r  r  r  r  )r  rY  r  r  r  rT    s   <rT  ("  __doc__Zsympy.externalr   r   r   r   r   r   Z%sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.integrals.rubi.symbolr  Zsympy.core.symbolr  r  Zsympy.functionsr  r  r  r  r  r  r  Z%sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  Z(sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  rW  ZA_ZB_ZC_r  ZG_ZH_r  r  Zc_r2  Ze_Zf_Zg_Zh_Zi_Zj_Zk_Zl_r  r  r'  Zq_Zr_Zt_r   r!  r  r$  r  Zy_Zz_Za1_Za2_Zb1_Zb2_Zc1_Zc2_Zd1_Zd2_Zn1_Zn2_Ze1_Ze2_Zf1_Zf2_Zg1_Zg2_Zn3_ZPq_ZPm_ZPx_ZQm_ZQr_ZQx_Zjn_Zmn_Znon2_ZRFx_ZRGx_r  iiZPqqQRr  Ckr  r  Z	ShowStepsZStepCounterrU  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r#  r%  r&  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  r  r  r  r  <module>   s              nJjB.
    
M


















































































































